Lead magnesium niobate—lead titanate (PMN-PT) exhibits exceptional electromechanical properties, considered as a highly efficient transduction material for vibration energy harvesting and acoustic sensing applications. It is reported in the literature that the PMN-PT undergoes structural phase transitions with changes in temperature and the chemical composition. We seek to gain insight into the phase diagram of PMN-PT using temperature and pressure dependence of the elastic properties. Single crystal PMN-PT with chemical composition close to the morphotropic phase boundary (MPB) was used in a resonant ultrasound spectroscopy (RUS) study performed in the temperature range from room temperature to 773 K and the pressure range from near vacuum to 3.4 MPa. At atmospheric pressure, significantly high acoustic attenuation of the PMN-PT material is observed at the temperatures below 400 K. Strong stiffening is observed in the temperature range of 400 K–673 K, followed by a gradual softening at higher temperatures. With the varying pressure, we observed an increased pressure sensitivity of elastic properties of the PMN-PT material that can be localized to the temperature regime where the strong stiffening is observed. As time allows, the behavior of PMN-PT upon cooling below room temperature will also be discussed.